The theory of electronically non-adiabatic processes in atom scattering on surfaces of solids, in particular metals, is reviewed. It is assumed that resonant tunnelling of electrons between an electronic orbital of the adatom and the conduction band of the substrate is the dominant charge exchange mechanism. The kinetic energy of the adatom is assumed to be in the intermediate range (eV to keV), which makes it possible to treat the adatom trajectory classically and to obtain a time-dependent electronic Hamiltonian. The aim of the theory is to find the deviations from adiabaticity, i.e. the fraction of the minority charge states of the atom after scattering and the spectrum of the electron-hole pairs created in the substrate. Under some simplifying approximations, these quantities can be calculated explicitly. Their dependence upon the adatom velocity and other parameters of the model is analysed, with particular attention paid to features which are characteristic of an extended substrate, in contrast to atom-atom or atom-molecule scattering. The present understanding of more complete models, for example inclusion of the intra-atomic Coulomb correlation, is also reviewed.